{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R95",
  "content_hash": null,
  "slug": "ca3153-claim-published-interval",
  "type": "claim",
  "title": "The checked published interval is 27 through 57",
  "summary": "The elementary interaction bound and a published 57-row construction give 27 <= CAN(3,15,3) <= 57; the exact value remains unresolved in the sources reviewed.",
  "relevance": "For Exact value of CAN(3,15,3), record ca3153-claim-published-interval (“The checked published interval is 27 through 57”) records a bound, answer, status fact, or structural consequence. The record states: The elementary interaction bound and a published 57-row construction give 27 <= CAN(3,15,3) <= 57; the exact value remains unresolved in the sources reviewed.",
  "relevance_source": "recorded",
  "body": "A strength-three ternary covering array with 15 columns must display all \\(3^3=27\\) ordered triples in every choice of three columns. One row supplies one triple for a fixed column choice, so every such array has at least 27 rows.\n\nAvila-George, Torres-Jimenez, Hernandez, and Gonzalez-Hernandez report 57 rows for \\(k=15\\) in Table 2(a) of their 2012 primary paper. Their table labels this value as the best-known solution before their cooperative simulated-annealing experiment and reproduces 57 in the experiment. This gives the sourced upper bound\n\\[\n27\\le \\operatorname{CAN}(3,15,3)\\le57.\n\\]\nThe paper says its arrays were deposited in the Cinvestav Covering Array Repository and verified with a separate tool. The repository now requires access, and the audit recovered no public 57-row payload or nonexistence certificate for 56 rows. The exact value should therefore remain open in TheoremDB.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the homogeneous ternary covering-array number CAN(3,15,3)",
    "bounds": {
      "strength": {
        "min": 3,
        "max": 3
      },
      "columns": {
        "min": 15,
        "max": 15
      },
      "alphabet_size": {
        "min": 3,
        "max": 3
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1155/2012/897027",
      "locator": "J. Avila-George, J. Torres-Jimenez, V. Hernandez, and N. Gonzalez-Hernandez, New Bounds for Ternary Covering Arrays Using a Parallel Simulated Annealing, Mathematical Problems in Engineering 2012, Article 897027, Table 2(a), row t=3 and k=15; repository and verification statement in Section 6"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1155/2012/897027",
    "locator": "J. Avila-George, J. Torres-Jimenez, V. Hernandez, and N. Gonzalez-Hernandez, New Bounds for Ternary Covering Arrays Using a Parallel Simulated Annealing, Mathematical Problems in Engineering 2012, Article 897027, Table 2(a), row t=3 and k=15; repository and verification statement in Section 6"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R94",
      "title": "The completed NIST 80-row array covers every interaction",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "covering-array-3-15-3",
      "title": "covering array 3 15 3",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}